Geodesic
Asymptotic behaviour of the solution of the singularly perturbed parabolic problem in the critical case
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 30 (1990) no. 6, pp. 858-867

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A zeroth-order boundary-layer asymptotic expansion is constructed and proved for solving a mixed boundary-value problem for a parabolic equation in the critical case. A smoothing procedure is applied to the nonsmooth terms of the asymptotic expansion when constructing the solution. 
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     author = {V. Yu. Buchnev},
     title = {Asymptotic behaviour of the solution of the singularly perturbed parabolic problem in the critical case},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {858--867},
     publisher = {mathdoc},
     volume = {30},
     number = {6},
     year = {1990},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_6_a5/}
}
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V. Yu. Buchnev. Asymptotic behaviour of the solution of the singularly perturbed parabolic problem in the critical case. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 30 (1990) no. 6, pp. 858-867. http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_6_a5/